6x^2+13x-14=0

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Solution for 6x^2+13x-14=0 equation:


Simplifying
6x2 + 13x + -14 = 0

Reorder the terms:
-14 + 13x + 6x2 = 0

Solving
-14 + 13x + 6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
-2.333333333 + 2.166666667x + x2 = 0

Move the constant term to the right:

Add '2.333333333' to each side of the equation.
-2.333333333 + 2.166666667x + 2.333333333 + x2 = 0 + 2.333333333

Reorder the terms:
-2.333333333 + 2.333333333 + 2.166666667x + x2 = 0 + 2.333333333

Combine like terms: -2.333333333 + 2.333333333 = 0.000000000
0.000000000 + 2.166666667x + x2 = 0 + 2.333333333
2.166666667x + x2 = 0 + 2.333333333

Combine like terms: 0 + 2.333333333 = 2.333333333
2.166666667x + x2 = 2.333333333

The x term is 2.166666667x.  Take half its coefficient (1.083333334).
Square it (1.173611113) and add it to both sides.

Add '1.173611113' to each side of the equation.
2.166666667x + 1.173611113 + x2 = 2.333333333 + 1.173611113

Reorder the terms:
1.173611113 + 2.166666667x + x2 = 2.333333333 + 1.173611113

Combine like terms: 2.333333333 + 1.173611113 = 3.506944446
1.173611113 + 2.166666667x + x2 = 3.506944446

Factor a perfect square on the left side:
(x + 1.083333334)(x + 1.083333334) = 3.506944446

Calculate the square root of the right side: 1.872683755

Break this problem into two subproblems by setting 
(x + 1.083333334) equal to 1.872683755 and -1.872683755.

Subproblem 1

x + 1.083333334 = 1.872683755 Simplifying x + 1.083333334 = 1.872683755 Reorder the terms: 1.083333334 + x = 1.872683755 Solving 1.083333334 + x = 1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = 1.872683755 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = 1.872683755 + -1.083333334 x = 1.872683755 + -1.083333334 Combine like terms: 1.872683755 + -1.083333334 = 0.789350421 x = 0.789350421 Simplifying x = 0.789350421

Subproblem 2

x + 1.083333334 = -1.872683755 Simplifying x + 1.083333334 = -1.872683755 Reorder the terms: 1.083333334 + x = -1.872683755 Solving 1.083333334 + x = -1.872683755 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.083333334' to each side of the equation. 1.083333334 + -1.083333334 + x = -1.872683755 + -1.083333334 Combine like terms: 1.083333334 + -1.083333334 = 0.000000000 0.000000000 + x = -1.872683755 + -1.083333334 x = -1.872683755 + -1.083333334 Combine like terms: -1.872683755 + -1.083333334 = -2.956017089 x = -2.956017089 Simplifying x = -2.956017089

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.789350421, -2.956017089}

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